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HomeworkSolutions_C4

# HomeworkSolutions_C4 - Problem#1 A differential manometer...

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Problem #1 : A differential manometer is used to measure the pressure difference two points in a pipe of varying cross-sectional area. If the manometric height is h, determine the velocity at point 1 (V1) and 2 (V2). Assume frictionless, steady, constant density flow. Answer: Assumptions: a. Neglect surface tension between the fluid and the mercury (Hg) b. Gradual reduction of the pipe between (1) and (2). Writing the steady flow Bernoulli equation, between (1) and (2) 2 2 1 2 1 1 2 1 1 2 2 f f p p u h u g g ρ ρ 2 h + + = + + where 1 2 2 1 2 1 (due to assumption (b)) (1) h h A u u A = and are the cross-sectional areas of the pipe at (1) and (2) respectively A 1 A 2 ( ) 1 2 Hg f p p g ρ ρ h = Δ Thus ( ) 2 2 1 2 1 2 1 2 f p p u u g ρ = − Or 2 2 2 2 1 1 1 1 2 Hg f A u h A ρ ρ = Δ Or

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